Summary: Bifurcations in turbulent rotating Rayleigh-Bénard
convection: A finite-size effect
Stephan Weiss and Guenter Ahlers
Department of Physics, University of California, Santa Barbara, CA 93106, USA
E-mail: guenter@physics.ucsb.edu
Abstract. In turbulent rotating Rayleigh-Bénard convection Ekman vortices extract hot or cold fluid from
thermal boundary layers near the bottom or top plate and enhance the Nusselt number. It is known from
experiments and direct numerical simulation on cylindrical samples with aspect ratio D/L (D is the
diameter and L the height) that the enhancement occurs only above a bifurcation point at a critical inverse
Rossby number 1/Roc, with 1/Roc 1/. We present a Ginzburg-Landau like model that explains
the existence of a bifurcation at finite 1/Roc as a finite-size effect. The model yields the proportionality
between 1/Roc and 1/ and is consistent with several other measured or computed system properties. Here
it is used to estimate the suppression of the heat-transport enhancement by the sidewall.
1. Introduction
It has long been known (Rossby, 1969) that heat transport, usually expressed in terms of the Nusselt
number Nu, in turbulent Rayleigh-Bénard convection can be enhanced significantly by rotating the
sample at modest rates about a vertical axis while the Rayleigh number Ra and the Prandtl number
Pr are held constant. It is well understood that this enhancement is caused by the Coriolis force, which
spins thermal plumes emanating from the thermal boundary layers near the top and bottom plates into
cyclonic vortex tubes known as Ekman vortices. These vortices extract additional warm (cold) fluid out of